3.1 Volume of Spheres

http://tube.geogebra.org/material/show/id/166700 (Download GeoGebra file)

The figure shows a hemisphere of radius r and a cylinder of base radius and height r with an inverted cone of the same height and base radius removed. Drag the red point to see the cross-sections of the two solids at a height h.

(a) Express x and y in terms of r and h.

(b) Are the cross-sections equal in areas?

(c) Hence show that the volume of the sphere of radius r is 4/3 π r³.